200=100x-2x^2

Solution for 200=100x-2x^2 equation:

200=100x-2x^2

We move all terms to the left:

200-(100x-2x^2)=0

We get rid of parentheses

2x^2-100x+200=0

a = 2; b = -100; c = +200;
Δ = b2-4ac
Δ = -1002-4·2·200
Δ = 8400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8400}=\sqrt{400*21}=\sqrt{400}*\sqrt{21}=20\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{21}}{2*2}=\frac{100-20\sqrt{21}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{21}}{2*2}=\frac{100+20\sqrt{21}}{4}
$